Heat oven to 325 degrees F and arrange racks in upper and lower third.
Combine flour and salt in a medium bowl and whisk until aerated and evenly combined; set aside.
Put butter in the bowl of a stand mixer fitted with the paddle attachment and mix over medium-high speed until light and fluffy, about 3 minutes. Add sugar and vanilla and continue to mix until whipped and light, about 2 more minutes.
Add half of the nuts and mix until evenly incorporated and nuts are broken up, about 1 minute. Add flour and mix until well combined, about 1 minute. Remove bowl from mixer and stir in remaining nuts.
Shape dough into 1-tablespoon balls and place on parchment-lined baking sheets, spaced at least 1 inch apart. Bake, rotating pans halfway through, until underside of cookies are brown, about 25 minutes. Remove from oven and let cool 5 minutes on baking sheets.
Meanwhile, put some powdered sugar in a medium bowl. After 5 minutes, roll the cookies in the powdered sugar until just coated and tap off excess. Let cool completely and recoat in powdered sugar, tapping off excess sugar, before serving.